Bayesics

Content for Tuesday, September 19, 2023

Content

  • Probability
  • Key concepts: prior, posterior and interpretation
  • Predictive distributions
  • Marginal likelihood and numerical integration
  • Credible intervals, loss functions and posterior summaries
  • The beta binomial conjugate model

Learning objectives

At the end of the chapter, students should be able to

  • define key notions (posterior distribution, posterior predictive, marginal likelihood, credible intervals) of Bayesian inference
  • perform inference in conjugate models with a single parameter
  • calculate and compute numerically summaries of posterior distributions (point estimators and credible intervals)
  • explain some of the conceptual differences between frequentist and Bayesian inference

Readings

Warning

These readings should be completed before class, to ensure timely understanding and let us discuss the concepts together through various examples and case studies — the strict minimum being the course notes.

Complementary readings

Warning

Complementary readings are additional sources of information that are not required readings, but may be useful substitutes. Sometimes, they go beyond the scope of what we cover and provide more details.

Slides

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References

Albert, J. (2009). Bayesian computation with R (2nd ed.). Springer. https://doi.org/10.1007/978-0-387-92298-0
Edwards, W., Lindman, H., & Savage, L. J. (1992). Bayesian statistical inference for psychological research. In S. Kotz & N. L. Johnson (Eds.), Breakthroughs in statistics: Foundations and basic theory (pp. 531–578). Springer. https://doi.org/10.1007/978-1-4612-0919-5_34
Johnson, A. A., Ott, M. Q., & Dogucu, M. (2022). Bayes rules! An introduction to applied Bayesian modeling (1st ed.). Chapman; Hall/CRC. https://doi.org/10.1201/9780429288340
Villani, M. (2023). Bayesian learning: A gentle introduction. https://mattiasvillani.com/BayesianLearningBook/